Tool to list the possible positions of a cube. A die is a cube with 6 differentiated faces, it can be defined by its visible faces so as to know its possible orientations / rotations.
Cube Rotation - dCode
Tag(s) : Fun/Miscellaneous
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Cube Rotation
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Tool to list the possible positions of a cube. A die is a cube with 6 differentiated faces, it can be defined by its visible faces so as to know its possible orientations / rotations.
Answers to Questions
How to list all rotations of the cube?
Place the cube on one side and orient it according to the 4 directions. Move to the next position (other side). And so on.
Example:
| - | 1 | - |
| 5 | 4 | 2 |
| - | 6 | - |
| - | 3 | - |
How to count all possible rotations of a cube?
The die can fall on one of the 6 faces possible and be oriented according to 4 angles, or 24 possibilities. $$ 6 \times 4 = 24 $$
Mathematically, how rotations of a cube are defined?
There are 4 types of rotation:
- Rotation according to the diagonals
- Rotation along the axis connecting the centers of 2 opposite faces
- Rotation along the axis connecting the centers of 2 opposite edges
- Identity rotation (original stationary state)
How to count all possible symmetries of a cube?
A cube whose faces are undifferentiated with 13 axes of symmetries:
- 3 axes pass through the centers of the faces, a cube has 6 faces, so 3 axes
- 6 axes pass through the centers of the opposite edges, a cube has 12 edges, so 6 axes
- 4 axes go through the opposite corners, a cube has 8 angles, so 4 axes
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Source code
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